Logistic Regression Method

An important feature of the logistic regression method is that although the input modelling data (P0) are binary, the calculated probability (P) is a continuous function. 

Logistic Regression Method for Occult (Internal Organ) Tumors (Dinse, 1985)... 

Nick TG, Campbell KM. Logistic regression. Methods Mol Biol. 2007 404 273-301. 

Chapter 9.5.1. in Ryan (2008)). In the case that the outcome is ordinal (i.e., good, better, best), another variant called ordered logistic regression is suitable. The logistic regression methods do not require normal distribution of the predictor variables (Tabacknick and Fidell, 1996, p. 575). 

This classification of bonds allowed the application of logistic regression analysis (LoRA), which proved of particular benefit for arriving at a function quantifying chemical reactivity. In this method, the binary classification (breakable or non-breakable, represented by 1/0, respectively) is taken as an initial probability P0, which is modelled by the following functional dependence (Eqs. 7 and 8) where f is a linear function, and x. are the parameters considered to be relevant to the problem. The coefficients c. are determined to maximize the fit of the calculated probability of breaking (P) as closely as possible to the initial classification (P0). 

Esposito Vinci, V., Tenenhaus, M. in Esposito Vinci, V., Lauro, C., Morineau, A., Tenenhaus, M. (Ed.), PLS and related methods. Proceedings of the PLS 01 International Symposium, CISIA-CERESTA, Paris, France, 2001, pp. 117-130. PLS Logistic Regression. 

One method that we have found particularly useful for our purposes is logistic regression analysis (LoRA). In this method, a binary classification is taken as a probability, Pq (given the value 0 or 1) and modelled by the two coupled equations 5 and 6. 

In Chapter 6 we covered methods for adjusted analyses and analysis of covariance in relation to continuous (ANOVA and ANCOVA) and binary and ordinal data (CMH tests and logistic regression). Similar methods exist for survival data. As with these earlier methods, particularly in relation to binary and ordinal data, there are numerous advantages in accounting for such factors in the analysis. If the randomisation has been stratified, then such factors should be incorporated into the analysis in order to preserve the properties of the resultant p-values. 

Hernandez-Caraballo et al. [91,92] evaluated several classical chemometric methods and ANNs as screening tools for cancer research. They measured the concentrations of Zn, Cu, Fe and Se in blood serum specimens by total reflection XRF spectrometry. The classical chemometric approaches used were PCA and logistic regression. On the other hand, two neural networks were employed for the same task, viz., back-propagation and probabilistic neural networks. 

The empirical models are based on mathematical functions that mimic the distribution of the standards measured in the assay. They can be based on point to point (interpolation) methods or regression methods. The most widely used empirical models that have been applied to MIP-ILAs include the log-logit model and the four-parameter logistic model. 

Arena VC, Sussman NB, Mazumdar S, Yu S, Macina OT. The utility of structure-activity relationship (SAR) models for prediction and covariate selection in developmental toxicity Comparative analysis of logistic regression and decision tree methods. SAR QSAR Environ Res 2004 15 1-18. 

The data obtained from NMR spectroscopy are generally complex, and thus multivariate statistical methods are often used to extract the maximum information from the large datasets. Of the multivariate methods, the most frequently used are principal component analysis (PCA), logistic regression,... 

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